I left my HP15C unused for several months and now cannot get it to work.
I have replaced the batteries but cannot get a display.
The batteries had not leaked and there is no physical damage to the calculator.
I have tried shorting out the battery terminals as per HP recommendation but this has not worked.
Can anyone give any guidance?

the only other "external" procedure, if you did not try it yet, is pressing [ON] and [yx] simultaneously. You can find this procedure in page 263 (Rev. E, Feb. 1984 eddition) under Veifying Proper Operation. The first step is exactly this.

If you have already tried this procedure, it's necessary to open the calculator because it probably need service. BTW, do you know/remember when it was bought? Can you post its serial #? That will help identifying which internal PCB does it have.

In many cases, simply re-soldering IC's terminals is enough to bring it back to life.

Before opening up the HP15C for surgery, there is one other possibility for this HP15C behavior. A fellow engineer in my office tried to resuscitate his HP15C with new batteries after a long hibernation, but after installing a new set of cells, he couldn't get it to start up, even after trying the various reset keystrokes and shorting the battery terminals. As a last resort, we switched batteries with those from my own HP15C, and his calculator started right up. The only difference we could find was that the new cells he had purchased were silver-oxide cells (SR44) while the cells I had in my calculator were alkaline cells (LR44). There is a slight difference in voltage, with the siver oxide cells having an open-circuit voltage of 1.55 -1.60 volts, while the alkaline cells have the typical 1.50 volts. Apparently his calculator did not like the slightly higher total voltage. My calculator, strangely, didn't seem to mind. We checked to make sure it wasn't a problem with dirty contacts, etc. so this was a little strange. You may wish to check which kind of cell you are using in the calculator, just in case.

I'm not so sure that differing voltages of 1.55-1.60 V versus 1.50 V should make any difference. I've found that any fresh cell, no matter what chemistry, will have a volatge slightly higher than rated value. 1.58 V is about right for a 1.5 V cell.